72
Statistical Methods for Estimating Petroleum Resources
Estimation of Exploration Effi ciency
Exploration effi ciency measures how fast explorationists can discover
the few largest pools in a play. During the past several decades, a number
of methods for estimating exploration effi ciency have been suggested.
The history of estimating exploration effi ciency merits a brief review.
Drilling effi ciency, C, as defi ned by Arps and Roberts (1958) is
discussed in Chapter 7 (see Eq. 7.4). Arps and Roberts classifi ed the
reasons for drilling a prospect into three classes and proposed that if
Table 4.4. Summary of the Estimates for Various Populations When n = 50
(Lognormal Assumption Is Not Used)
Types of
populations
Total
resources
N
ˆ
N
ˆ
β
Upper percentiles
95
75
50
25
5
Lognormal
50,901 300 300 0.6 40,813 49,407 56,926 66,014
80,416
Weibull
6100 300 300 0.6
5563
5939
6221
6493
6913
Pareto
30,375 300 260 0.6 16,629 22,405 26,504 31,287 38,849
Mixture
of two
lognormals
35,526 300 300 1.0 18,474 25,577 32,599 43,826
56,071
Mixtures of
lognormal,
Weibull,
and Pareto
32,333 300 300 0.8 18,182 24,792 30,623 37,371 48,040
Table 4.3. Summary of the Estimates for Various Populations When n = 30
(Lognormal Assumption Is Not Used)
Types of
populations
Total
resources
N
ˆ
N
ˆ
β
Upper percentiles
95
75
50
25
5
Lognormal
50,901 300 300 0.6 27,944 33,549 38,456 45,181
57,801
Weibull
6100 300 280 1.4
1983
2228
2405
2599
2883
Pareto
30,375 300 220 0.6
9241 14,119 17,995 22,179
29,212
Mixture
of two
lognormals
35,526 300 300 1.2 12,300 19,295 25,412 32,851 44,841
Mixtures of
lognormal,
Weibull,
and Pareto
32,333 300 300 0.6 20,099 26,642 32,324 39,050
49,842
Statistical Methods for Estimating Petroleum Resources
Estimation of Exploration Effi ciency
Exploration effi ciency measures how fast explorationists can discover
the few largest pools in a play. During the past several decades, a number
of methods for estimating exploration effi ciency have been suggested.
The history of estimating exploration effi ciency merits a brief review.
Drilling effi ciency, C, as defi ned by Arps and Roberts (1958) is
discussed in Chapter 7 (see Eq. 7.4). Arps and Roberts classifi ed the
reasons for drilling a prospect into three classes and proposed that if
Table 4.4. Summary of the Estimates for Various Populations When n = 50
(Lognormal Assumption Is Not Used)
Types of
populations
Total
resources
N
ˆ
N
ˆ
β
Upper percentiles
95
75
50
25
5
Lognormal
50,901 300 300 0.6 40,813 49,407 56,926 66,014
80,416
Weibull
6100 300 300 0.6
5563
5939
6221
6493
6913
Pareto
30,375 300 260 0.6 16,629 22,405 26,504 31,287 38,849
Mixture
of two
lognormals
35,526 300 300 1.0 18,474 25,577 32,599 43,826
56,071
Mixtures of
lognormal,
Weibull,
and Pareto
32,333 300 300 0.8 18,182 24,792 30,623 37,371 48,040
Table 4.3. Summary of the Estimates for Various Populations When n = 30
(Lognormal Assumption Is Not Used)
Types of
populations
Total
resources
N
ˆ
N
ˆ
β
Upper percentiles
95
75
50
25
5
Lognormal
50,901 300 300 0.6 27,944 33,549 38,456 45,181
57,801
Weibull
6100 300 280 1.4
1983
2228
2405
2599
2883
Pareto
30,375 300 220 0.6
9241 14,119 17,995 22,179
29,212
Mixture
of two
lognormals
35,526 300 300 1.2 12,300 19,295 25,412 32,851 44,841
Mixtures of
lognormal,
Weibull,
and Pareto
32,333 300 300 0.6 20,099 26,642 32,324 39,050
49,842